Robot machining parameter optimization method and system based on global stability analysis

Abstract

A robot machining parameter optimization method and system based on global stability analysis solves the problem of how to improve the efficiency of global stability analysis of robot milling. The invention belongs to the technical field related to robot milling. The invention includes: extracting the tool position related to the cutting process, selecting the reference tool position, calculating the stability limit reference data set under the robot reference tool position based on the frequency response function and the robot dynamics model; when analyzing the stability, obtaining the axial cutting depth a of the jth tool position p,j , and find the stability axial cutting depth limit a with the same or closest feed direction and radial cutting width as the j-th tool position in the stability limit reference data set p,lim,0 , according to a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j , according to a p,j and a p,lim,j The ratio of is used to determine whether there is chatter at any tool position, and all tool positions can meet the stable machining requirements by adjusting the parameters.

Description

Technical Field

[0001] The present invention relates to a robot machining parameter optimization method and system based on global stability analysis, belonging to the technical field related to robot milling machining. Background Art

[0002] In recent years, with the improvement of the static and dynamic performance of industrial robots, robotic milling systems have been increasingly used to machine local features on large, complex structural components in fields such as aviation, aerospace, and energy. Due to their low structural stiffness, robots are prone to low-frequency chatter when stimulated by milling forces, resulting in poor milling quality and efficiency. By establishing a chatter prediction model for robotic milling and optimizing the robot's machining posture and process parameters, chatter can be effectively suppressed, thereby improving machining efficiency.

[0003] Regarding low-frequency chatter in robotic milling, Pan et al. published a paper in 2006 titled "Chatter analysis of robotic machining process," which argues that low-frequency chatter in robots is modal coupling chatter, and proposed a coupled chatter stability criterion by simplifying the milling dynamics model. The invention patent with publication number CN113894782A, "Method and system for optimizing the posture of robotic milling based on stiffness orientation," calculates the difference between the two main stiffnesses at the tool tip under different joints and tool axis vectors of the robot system, and determines the division between the stable workspace and the potential chatter workspace, avoiding chatter by optimizing the robot's redundant angle. The invention patent with publication number CN111633650A, "A modal coupling chatter suppression method based on robot stiffness characteristics," discloses a method and system for optimizing the posture of robotic milling based on stiffness orientation.

[0004] Patent publication number CN112380726A establishes a two-degree-of-freedom modal coupling dynamics equation and stability criteria to determine whether the initially set robot posture and spindle feed direction are stable. It then adjusts unstable robot postures or spindle feed directions to achieve modal coupling chatter suppression. Both of these studies and inventions utilize the modal coupling principle for stability analysis.

[0005] The paper "Can mode coupling chatter happen in milling" published by Celikag et al. in 2021 established modal coupling and regenerative chatter prediction models respectively, and proved through milling experiments that the mechanism of low-frequency chatter of the robot is regenerative chatter, not modal coupling chatter mechanism. The invention patent with publication number CN115945725A "A six-degree-of-freedom robot milling stability prediction method and system" established a dynamic model considering the feed rate and performed stability prediction based on the full discrete method. The invention patent with publication number CN115890345A "A robot milling low-frequency chatter stability prediction method and system" calculates dynamic cutting thickness based on surface update (SR), adopts a dynamic modeling strategy based on the impulse response function method (IRF), combines SR and IRF, and considers the intermittent cutting characteristics of milling and modal coupling effects at the same time, and establishes a stability prediction method based on time domain simulation.

[0006] Stability analysis based on regenerative chatter mechanisms requires obtaining an accurate frequency response function (FRF) and employing methods such as semi-discrete methods and time-domain simulation. Because the robot's FRF is affected by factors such as its position, feed rate, and external load, traditional methods for performing global stability analysis on machining programs containing tens of thousands of points require obtaining the robot's FRF data for each point, and these stability analysis methods are computationally very time-consuming. These factors limit the use of traditional methods for global stability analysis in robotic milling machining. Summary of the Invention

[0007] In order to solve the problem of how to improve the efficiency of global stability analysis of robot milling processing, the present invention provides a robot processing parameter optimization method and system based on global stability analysis.

[0008] A robot machining parameter optimization method based on global stability analysis of the present invention comprises:

[0009] S1. Obtain a machining program for a given workpiece. For the machining program in a given workpiece coordinate system, extract the cutting process program, determine all tool position points in the cutting process program, and calculate the coordinate transformation matrix of each tool position point corresponding to the feed coordinate system.

[0010] S2. Combined with the robot dynamics model, calculate the frequency response function Φ of each tool position in the robot flange coordinate system rs (ω), the coordinate transformation matrix obtained by S1 is used to transform the frequency response function Φ rs (ω) is converted to the feed coordinate system, and Φ is obtained en (ω);

[0011] S3, select a tool position in the cutting process program as the reference tool position, and use the robot kinematics model to solve the Φ corresponding to the reference tool position. en (ω), according to the Φ en (ω) Using the milling stability prediction method, the stability axial depth of cut limit under different feed directions and radial cutting widths at the robot reference tool position is calculated. The stability axial depth of cut limit is the maximum axial cutting depth at which the tool position does not vibrate. The stability axial depth of cut limits under different feed directions and radial cutting widths are combined into a stability limit reference data set.

[0012] S4. Get the axial cutting depth a of the jth tool position in the machining program of a given workpiece p,j , and find the stability axial cutting depth limit a with the same or closest feed direction and radial cutting width as the j-th tool position in the stability limit reference data set p,lim,0 , according to the stability axial cutting depth limit a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j , according to a p,j and a p,lim,j The ratio of is used to determine whether there is a tool position that will vibrate. If there is a tool position that will vibrate, adjust the feed direction, cutting width and feed depth of the tool position in sequence, and repeat S1-S4 until all tool positions do not vibrate.

[0013] Preferably, S1 further includes:

[0014] According to the intervals between adjacent tool positions in the cutting process program, the tool positions with long intervals in the cutting process program are found, and new tool positions are inserted between the tool positions with long intervals using an equal interval interpolation algorithm.

[0015] Preferably, the cutting process program includes all tool positions between the last tool position of the cutting-in phase and the last tool position of the machining process.

[0016] As a preference, the frequency response function Φ rs (ω) is:

[0017]

[0018] Among them, M rs 、 and K rs are the mass matrix, damping matrix and stiffness matrix of the robot in Cartesian space; M rs =J -T M q J -1 , K rs =J -T K q J-1 ; J is the Jacobian matrix, M q 、 and K q They are the moment of inertia matrix, joint damping matrix and joint stiffness matrix of the robot in the joint space;

[0019] The frequency response function Φ rs (ω) is converted to the feed coordinate system, and Φ is obtained en (ω):

[0020]

[0021] in, is the rotation matrix from the feed coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the workpiece coordinate system, is the rotation matrix from the workpiece coordinate system to the tool feed coordinate system.

[0022] As a preference, in S2, according to Φ en (ω) and Use the semi-discrete method or the full-discrete method to calculate the stability axial cutting depth limit a under different feed directions and radial cutting widths at the reference tool position of the robot p,lim,0 , constitutes the stability limit reference data set; among them, G L is the stability coefficient, u(t)=[x(t),y(t),z(t)] T , x(t), y(t), z(t) are the three-axis components of the tool tip vibration displacement at time t; T represents the time period.

[0023] As a preference, according to the stability axial cutting depth limit a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j :

[0024]

[0025] θ e,j ,θ s,j represents the tool entry angle and tool exit angle at the jth tool position, C en is the flexibility parameter in the normal direction of the tool-workpiece meshing area, C en,x,j 、C en,y,j C at the j-th knife point en The x- and y-axis components of ψ n,j is the directional frequency response function at the jth tool position; θ e,0 ,θ s,0 Indicates the tool entry angle and tool exit angle at the reference pose, Cen,x，0 、C en,y,0 They are respectively at the reference pose C en The x- and y-axis components of ψ n,0 is the directional frequency response function at the reference pose;

[0026] As a preference, according to the j-th tool position coordinate value, the joint angle, Jacobian matrix, and joint stiffness matrix are calculated through the robot kinematics model to obtain C en,x,j and C en,y,j :

[0027] The flexibility parameter C at the j-th tool point en for

[0028] Among them, C rs,tt Represents the translation stiffness matrix, through the global stiffness matrix Get, C θ is the joint stiffness matrix, C rs,rr represents the torsional stiffness matrix, C rs,tr represents the translation-torsion coupling matrix, C rs,rt represents the torsional-translational coupling matrix.

[0029] As a preference, a p,j and a p,lim,j The ratio is:

[0030]

[0031] Among them, PI f Indicates the probability of chatter occurrence at the corresponding tool position. When PI f When the value is less than the threshold, chattering occurs. The threshold value range is 1-1.1.

[0032] The present application also provides a computer-readable storage device, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the above-mentioned robot processing parameter optimization method based on global stability analysis.

[0033] The present application also provides a robot processing parameter optimization system based on global stability analysis, including a storage device, a processor, and a computer program stored in the storage device and executable on the processor. The processor executes the computer program to implement the steps of the robot processing parameter optimization method based on global stability analysis as described above.

[0034] The beneficial effects of the present invention are as follows: (1) Based on the frequency response function of the robot reference posture, the present invention uses the frequency response function of a reference tool position and the predicted axial cutting depth limit as a reference to obtain a reference data set of stability limits for different feed directions and radial cutting widths. It is used to quickly calculate the stability prediction of the processing program. This method simplifies some conditions and does not require the calculation of the precise frequency response function for each robot posture corresponding to the program, thereby reducing the calculation time, improving the efficiency of process planning, and effectively promoting the application of this technology. (2) The present invention effectively preprocesses the robot processing program. The obtained processing program is usually a mixture of long and short intervals between adjacent tool positions. The dynamic characteristics of the robot end at different positions are different, so the first and last tool positions with long intervals cannot accurately reflect the dynamic characteristic changes of all points in the processing process. The present invention interpolates the long intervals in the processing program to accurately perform global stability analysis. (3) The present invention proposes a process parameter optimization method for optimizing feed direction, axial cutting depth and radial cutting width, while the existing method does not focus on the optimization effect of radial cutting width. According to the indicators and optimization method of the present invention, the optimal radial cutting width with both efficiency and stability can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a robot milling processing parameter optimization method based on global stability analysis provided by the present invention;

[0036] Figure 2 The two-degree-of-freedom milling dynamics system involved in an embodiment of the present invention includes: (a) the conversion relationship between the frequency response function in the tool coordinate system and the frequency response function in the feed coordinate system; (b) the conversion relationship between the frequency response function in the feed coordinate system and the directional frequency response function;

[0037] Figure 3 is a design drawing of a contour sample involved in an embodiment of the present invention;

[0038] Figure 4 The tool paths generated by different contour area clearing strategies involved in the embodiments of the present invention;

[0039] Figure 5 1 is the stability analysis result of the roughing program generated by different milling strategies involved in the embodiment of the present invention, (a) offset milling strategy 1, (b) offset milling strategy 2, (c) parallel clearing strategy 1, (d) parallel clearing strategy 2;

[0040] Figure 6 is a low-frequency milling chatter detection result during rough machining according to an embodiment of the present invention;

[0041] Figure 7 1 is the stability analysis result of the finishing program involved in the embodiment of the present invention, wherein (a) the best contour finishing strategy 1, (b) the best contour finishing strategy 2;

[0042] Figure 8 These are the stability limits and experimental results under different radial cutting widths involved in the embodiments of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0044] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0046] The purpose of this embodiment is to use the proposed stability index to perform a global stability analysis of all tool positions in the machining program, and to suppress the chatter of tool positions where chatter occurs by modifying process parameters such as feed direction, radial cutting width, and axial cutting depth, thereby improving the robot's machining accuracy and efficiency.

[0047] To achieve the above objectives, the present invention proposes a robot machining parameter optimization method based on global stability analysis, comprising the following steps:

[0048] Step 1: Use CAM software to generate a machining program for a specified workpiece. Extract the cutting process program from the machining program in the given workpiece coordinate system. Using a given arc length search algorithm, the cutting process program is divided into long-interval tool points and short-interval tool points based on the spacing between adjacent tool points. New tool points are inserted between the long-interval tool points using an evenly spaced interpolation algorithm.

[0049] Specifically, in step 1, the processing program is divided into an idle run program, a cutting phase program, and a cutting process program through a character search function.

[0050] The tool points between the first tool point in the dry run program and the last tool point in the cut-in phase program are not analyzed. However, stability analysis is performed from the last tool point in the cut-in phase program to the last tool point in the machining process. Interpolation is then performed at equal intervals to obtain new interpolation points.

[0051] Furthermore, the transformation matrix between the workpiece coordinate system of the tool position point and the feed coordinate system corresponding to each tool position point is calculated according to the following method:

[0052] Translation Matrix Conversion

[0053] Where, is the position in the cutting process program. It is calculated based on two adjacent knife position points. x 、o y 、o z Indicates the coordinate system value of the tool position corresponding to the z-axis of the feed coordinate system, v x 、v y 、v z Indicates the coordinate system value of the tool position corresponding to the y-axis of the feed coordinate system, u x 、u y 、u z Indicates the coordinate system value of the tool position corresponding to the x-axis of the feed coordinate system, Indicates the position of the tool position point corresponding to the origin of the feed coordinate system in the workpiece coordinate system.

[0054] Step 2: Calculate the frequency response function Φ in the flange coordinate system based on the robot dynamics model rs (ω), through coordinate transformation, Φ rs (ω) is converted to the feed coordinate system, and Φ is obtained en (ω).

[0055] Specifically, to calculate the frequency response function of each tool position, the dynamic model of the robot end in Cartesian space is rewritten in the frequency domain as follows:

[0056]

[0057] Where M rs 、 and K rs are the mass matrix, damping matrix, and stiffness matrix of the robot in Cartesian space;

[0058]

[0059] J is the Jacobian matrix, M q 、 and K q They are the moment of inertia matrix, joint damping matrix and joint stiffness matrix of the robot in the joint space;

[0060] In this step, the frequency response function of the robot flange coordinate system is converted to the feed coordinate system, and stability analysis is performed in the tool feed coordinate system. The robot frequency response function is converted from the flange coordinate system to the tool feed coordinate system using the following formula:

[0061]

[0062] Where, is the rotation matrix from the feed coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the workpiece coordinate system, is the rotation matrix from the workpiece coordinate system to the tool feed coordinate system.

[0063] Step 3: Select a tool position in the cutting process program as the reference tool position, and use the robot kinematics model to solve the Φ corresponding to the reference tool position. en (ω), according to the Φ en (ω) The milling stability prediction method is used to calculate the stability axial cutting depth limit under different feed directions and radial cutting widths at the robot reference tool position. The stability axial cutting depth limit is the maximum axial cutting depth without chatter at the tool position. The stability axial cutting depth limits under different feed directions and radial cutting widths are combined to form a stability limit reference data set.

[0064] Specifically, the method for obtaining the stability limit reference data set in step 3 is as follows:

[0065] Select the reference tool position of the robot, which can be specific or random, and use the robot kinematic model to calculate the frequency response function of the reference tool position in the flange coordinate system. For a specified feed direction, the angle between the feed direction and the x-axis of the workpiece coordinate system can be obtained, thereby calculating the Φ under different feed directions. rs (ω).

[0066] According to Φ rs (ω) Determine M rs 、 and K rs ;

[0067] Then get G L is the stability coefficient, u(t)=[x(t),y(t),z(t)] T , x(t), y(t), z(t) are the three-axis components of the tool tip vibration displacement at time t; T represents the time period;

[0068] Use the semi-discrete method or the full-discrete method to calculate the stability axial cutting depth limit a under different feed directions and radial cutting widths at the reference tool position of the robot p,lim,0 , constituting a stability limit reference data set.

[0069] Step 4: Get the axial cutting depth a of the jth tool position in the machining program of a given workpiece p,j , and find the stability axial cutting depth limit a with the same or closest feed direction and radial cutting width as the j-th tool position in the stability limit reference data setp,lim,0 , according to the stability axial cutting depth limit a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j , according to a p,j and a p,lim,j , determine whether there is any tool position that will vibrate. If there is a tool position that will vibrate, adjust the feed direction, cutting width and feed depth of the tool position in sequence, and repeat steps 1 to 4 until all tool positions do not vibrate.

[0070] Specifically, step 4 can propose a relative stability index based on the tooth averaging method and the stiffness model, and find the stability axial cutting depth limit a that is the same as or closest to the j-th tool position in feed direction and radial cutting width according to the stability limit reference data set. p,lim,0 , obtain the axial cutting depth a of the jth tool position in the machining program of a given workpiece p,j , calculate the probability of chatter occurrence at the jth tool position. When calculating the tool position stability limit, the ratio of the stability limit of different parameters to the reference stability limit of the corresponding feed direction and radial cutting width is used as the optimization index, a p,j and a p,lim,j The ratio is:

[0071]

[0072] Where PI f Indicates the probability of chatter occurrence at the corresponding tool position. When PI f When the value is less than the threshold, it means that chattering occurs. f When it is greater than the threshold, it means that the stability of the tool position meets the requirements. The threshold value is 1-1.1. p,j is the axial cutting depth of the jth tool position in the machining program of a given workpiece, a p,lim,j is the stability axial cutting depth limit of the j-th tool position.

[0073] When chatter occurs at a tool position, adjust the feed direction, cutting width, and feed depth in sequence, and repeat steps 1 to 4 until all tool positions meet the stability requirements.

[0074] In step 4, a relative stability index is proposed based on the tooth average method and the stiffness model. The specific process includes:

[0075] According to the average tooth angle method, the stability limit of the specified process parameters is calculated as follows:

[0076]

[0077] Among them, N t Indicates the number of teeth of the tool, k sis the force coefficient, which is calibrated by experiment or using the tool manufacturer’s recommended value; R e (ψ n ) is the real part of the directional frequency response function in the feed coordinate system at the tool position point in the normal direction of the tool-workpiece meshing area; θ e Indicates the tool cutting angle at the tool position; θ s Indicates the tool cutting angle at the tool position; when R e (ψ n ) is a negative number, the above formula has practical significance.

[0078] Directional frequency response function φ in the normal direction of the tool-workpiece meshing area n It can be calculated by the following formula:

[0079] φ n =φ en,x cos 2 (ψ n )+φ en,y sin 2 (ψ n )

[0080] Where, ψ n is the angle between the directional frequency response function and the Y axis (°); φ en,x is the frequency response function of the tool position point in the X direction in the feed coordinate system; φ en,y is the frequency response function of the tool position point in the Y direction in the feed coordinate system.

[0081] For down milling, ψ n It can be calculated by the following formula:

[0082]

[0083] Where β is the angle of the milling force relative to the surface normal direction; θ s is the tool cutting angle; θ e is the cutting angle of the tool; a e R is the radial cutting width; tool is the tool radius.

[0084] For a single degree of freedom system, φ n The minimum real part of can be approximated as:

[0085]

[0086] Among them, C n is the flexibility parameter in the normal direction of the tool-workpiece meshing area, and ξ is the damping ratio.

[0087] Based on the above analysis, the stability limit of the process parameters specified by the average tooth angle method can be simplified as follows:

[0088]

[0089] Combined with the simplified formula of stability limit, calculate a p,lim,0 and a p,lim,j In practical applications, the influence of the damping ratio ξ can be ignored. Therefore, the c lim is a constant, so we get a p,lim,0 and a p,lim,j The relationship between the stability of the axial cutting depth limit a of the j-th tool position is obtained. p,lim,j The expression:

[0090]

[0091] Among them, θ e,j ,θ s,j represents the tool entry angle and tool exit angle at the jth tool position, C en is the flexibility parameter in the normal direction of the tool-workpiece meshing area, C en,x,j 、C en,y,j C at the j-th knife point en The x- and y-axis components of ψ n,j is the directional frequency response function at the jth tool position; θ e,0 ,θ s,0 Indicates the tool entry angle and tool exit angle at the reference pose, C en,x，0 、C en,y,0 They are respectively at the reference pose C en The x- and y-axis components of ψ n,0 is the directional frequency response function at the reference pose;

[0092] When analyzing stability specifically, given the feed direction and radial cutting width parameters of the j-th tool position, find the stability axial cutting depth limit a with the same or closest feed direction and radial cutting width as the j-th tool position in the stability limit reference data set. p,lim,0 , combined with the above formula, the stability axial cutting depth limit a of the jth tool position can be obtained. p,lim,j ;

[0093] According to the coordinate value of the jth tool position, the joint angle, Jacobian matrix, and joint stiffness matrix are calculated through the robot kinematic model to obtain C en,x,j and C en,y,j :

[0094] The flexibility parameter C at the j-th tool point en for

[0095] Among them, C rs,ttRepresents the translation stiffness matrix, through the global stiffness matrix Get, C θ is the joint stiffness matrix, C rs,rr represents the torsional stiffness matrix, C rs,tr represents the translation-torsion coupling matrix, C rs,rt represents the torsional-translational coupling matrix.

[0096] Where θ e,j ,θ s,j ,C en,x,j ,C en,y,j ,ψ n,j etc. are the parameters of the j-th knife position, θ e,0 ,θ s,0 ,C en,x,0 ,C en,y,0 ,ψ n,0 are the reference parameters in the stability limit reference data set, respectively.

[0097] The present invention is further described in detail below with reference to the following examples.

[0098] The KR500 milling robot of KUKA was used as the object to verify this method.

[0099] To validate the proposed global stability optimization method, a series of milling experiments were carried out.

[0100] Considering that industrial robots are generally used for machining local features on large structural components with low precision requirements, this embodiment of the present invention draws on the contour machining specimen M1-160 specified in GB / T 34880.2-2017 to design a contour sample. This sample includes a variety of typical features, including holes, faces, prisms, squares, and bevels. The machining of this sample involves three processes: roughing, finishing, and hole machining. This embodiment of the present invention uses roughing and finishing as examples to calculate machining errors and analyze stability.

[0101] The workpiece material used in the embodiment of the present invention is aluminum alloy 6061-T6, and a vortex tube is used to cool the compressed air to improve the air cooling effect of the tool. To improve the cooling effect, a small amount of coolant is manually sprayed on the tool at intervals during the milling process.

[0102] The embodiment of the present invention uses the robot KSS control core for processing. Use 3D modeling software to build Figure 3A 3D model of the designed sample was then used to generate KRL programs for roughing and finishing using CAM software. The smoothing error of the tool paths generated by the CAM software was 0.1 mm. A 10 mm diameter, three-tooth carbide end mill was used for the experiment, and cutting parameters were determined based on stability analysis results. A post-processing module was developed using Python to identify, compensate, perform stability analysis, and update the KRL programs.

[0103] like Figure 4 As shown in Figure 2, robot rough machining adopts contour area clearing strategy, including parallel and offset clearing strategies. Figure 4 The offset milling strategy shown in (a) is the most commonly used milling strategy. It significantly reduces the number of tool lifts and feeds, thereby reducing the robot's idle running time and improving processing efficiency. Figure 4 The parallel removal strategy (shown in (b)) feeds the tool in a specific direction, which increases the number of tool lifts and feeds. Therefore, under the same cutting parameters, the parallel removal strategy takes longer to process than the offset removal strategy. However, the parallel removal strategy allows the operator to optimize the feed direction to suppress chatter.

[0104] In the embodiment of the present invention, several cutting experiments are conducted on a rough workpiece, the robot joint torque signal is collected, the milling force under different parameters and positions is calculated and used to identify the cutting force coefficient.

[0105] The embodiment of the present invention determines a combination of radial cutting width and axial cutting depth parameters according to a steady-state lobe diagram, thereby meeting the chatter-free requirement of all machining procedures.

[0106] The robot's frequency response function is affected by its position, feed direction, and operating state. Furthermore, machining programs contain tens of thousands of program points and different feed directions, making point-by-point stability analysis difficult to implement in practice. Because the damping ratio increases during robot operation, the robot's actual stability limit is often higher than that predicted using the stationary frequency response function. Considering practical needs and engineering applications, the stationary frequency response function can be used to predict the stability limit.

[0107] Considering the contour milling requirements of the sample, try to keep most of the trajectory within the feed angle range of 0-45°.

[0108] A semi-discrete method is used to calculate the stability limit of each tool position at a specified spindle speed, with calculation times generally ranging from 150ms to 200ms. Using the reference pose as a reference, the relative stability limit of the machining program point in the current feed direction is calculated in under 1ms, significantly reducing calculation time and improving process planning efficiency.

[0109] The stability analysis of the roughing program was conducted for different milling strategies and different process parameters. The analysis results are shown in Figure 5When low-frequency chattering dominated by the robot mode occurs, the value is 1; when high-frequency chattering dominated by the tool mode occurs, the value is -1; when stable cutting occurs, the value is 0.

[0110] like Figure 5 As shown in (a), there are many tool positions in the machining program of offset milling strategy 1 where low-frequency chatter may occur. When the radial cutting width is changed to 1mm, Figure 5 All tool positions of the offset milling strategy 2 shown in (b) meet the stability requirements, but the machining time increases by 2 times. Figure 5 As shown in (c) and the table above, Parallel Removal Strategy 1 has the same cutting parameters as Offset Removal Strategy 1, but its machining time is longer. Offset Removal Strategy 1 has chatter, while Parallel Removal Strategy 1 does not. Compared to Offset Removal Strategy 2, which also has no chatter, Parallel Removal Strategy 1 reduces machining time by approximately 47%. Figure 5 As shown in (d), no chatter occurs at any program point in parallel milling strategy 2.

[0111] Figure 6 The results of low-frequency milling chatter detection during rough machining according to the present invention are shown. R It is the chatter index set by the chatter detection system. When it is higher than this index, it means that chatter occurs in the milling process. Figure 5 The results show that no chatter occurs during the entire milling process.

[0112] Figure 7 The stability analysis results of the finishing program involved in the embodiment of the present invention are shown. Taking the calculation results of the program poses from 2329 to 2331 as an example, the coordinates of the 2329th and 2330th points are [84.996, 50.205, -24] and [84.996, -80.205, -24] respectively, CSI R It is the machining program point of side H. Figure 7 As shown in (a), a small number of tool positions in the optimal contour finishing strategy 1 will vibrate. After the line spacing is changed to 2mm, the stability analysis of the machining program of the optimal contour finishing strategy 2 is carried out, and the prediction results are shown in Figure 7 In (b), there is no chatter tool position in the machining program under these parameters.

[0113] Figure 8 The stability limits and experimental results under different radial cutting widths are shown, among which PI f Is a stability index. When it is greater than 1, it means that the robot can perform stable milling under this parameter. When it is less than 1, it means that chatter will occur. In order to verify the effectiveness of the proposed method, large radial cutting width parameters (12mm and 16mm) with higher efficiency are selected. Figure 8As shown, the preferred radial width of cut does not experience chatter when the axial depth of cut is 10 mm (below the predicted stability limit) and 15 mm (above the predicted stability limit).

[0114] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A robot machining parameter optimization method based on global stability analysis, characterized in that: The method comprises: S1. Obtain a machining program for a given workpiece. For the machining program in a given workpiece coordinate system, extract the cutting process program, determine all tool position points in the cutting process program, and calculate the coordinate transformation matrix of each tool position point corresponding to the feed coordinate system. S2. Combined with the robot dynamics model, calculate the frequency response function Φ of each tool position in the robot flange coordinate system rs (ω), the coordinate transformation matrix obtained by S1 is used to transform the frequency response function Φ rs (ω) is converted to the feed coordinate system, and Φ is obtained en (ω); S3, select a tool position in the cutting process program as the reference tool position, and use the robot kinematics model to solve the Φ corresponding to the reference tool position. en (ω), according to the Φ en (ω) Using the milling stability prediction method, the stability axial depth of cut limit under different feed directions and radial cutting widths at the robot reference tool position is calculated. The stability axial depth of cut limit is the maximum axial cutting depth at which the tool position does not vibrate. The stability axial depth of cut limits under different feed directions and radial cutting widths are combined into a stability limit reference data set. S4. Get the axial cutting depth a of the jth tool position in the machining program of a given workpiece p,j , and find the stability axial cutting depth limit a with the same or closest feed direction and radial cutting width as the j-th tool position in the stability limit reference data set p,lim,0 , according to the stability axial cutting depth limit a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j , according to a p,j and a p,lim,j The ratio of is used to determine whether there is a tool position that will vibrate. If there is a tool position that will vibrate, adjust the feed direction, cutting width and feed depth of the tool position in sequence, and repeat S1-S4 until all tool positions do not vibrate.

2. The robot processing parameter optimization method based on global stability analysis according to claim 1 is characterized in that: Said S1 further comprises: According to the intervals between adjacent tool positions in the cutting process program, the tool positions with long intervals in the cutting process program are found, and new tool positions are inserted between the tool positions with long intervals using an equal interval interpolation algorithm.

3. The robot processing parameter optimization method based on global stability analysis according to claim 1 is characterized in that: The cutting process program includes all tool positions between the last tool position of the cutting phase and the last tool position of the machining process.

4. The robot processing parameter optimization method based on global stability analysis according to claim 1 is characterized in that: Frequency response function Φ rs (ω) is: Among them, M rs 、 and K rs are the mass matrix, damping matrix and stiffness matrix of the robot in Cartesian space; M rs =J -T M q J -1 , K rs =J -T K q J -1 ; J is the Jacobian matrix, M q 、 and K q They are the moment of inertia matrix, joint damping matrix and joint stiffness matrix of the robot in the joint space; The frequency response function Φ rs (ω) is converted to the feed coordinate system, and Φ is obtained en (ω): in, is the rotation matrix from the feed coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the flange coordinate system, is the rotation matrix from the robot base coordinate system to the workpiece coordinate system, It is the rotation matrix from the workpiece coordinate system to the tool feed coordinate system.

5. The robot processing parameter optimization method based on global stability analysis according to claim 4 is characterized in that: In S2, according to Φ en (ω) and Use the semi-discrete method or the full-discrete method to calculate the stability axial cutting depth limit a under different feed directions and radial cutting widths at the reference tool position of the robot p,lim,0 , constituting a stability limit reference data set; Among them, G L is the stability coefficient, u(t)=[x(t),y(t),z(t)] T , x(t), y(t), z(t) are the three-axis components of the tool tip vibration displacement at time t; T represents the time period.

6. The robot processing parameter optimization method based on global stability analysis according to claim 1 is characterized in that: According to the stability axial cutting depth limit a p,lim,0 Calculate the stability axial cutting depth limit a of the jth tool position p,lim,j : Among them, θ e,j ,θ s,j represents the tool entry angle and tool exit angle at the jth tool position, C en is the flexibility parameter in the normal direction of the tool-workpiece meshing area, C en,x,j 、C en,y,j C at the j-th knife point en The x- and y-axis components of ψ n,j is the directional frequency response function at the jth tool position; θ e,0 ,θ s,0 Indicates the tool entry angle and tool exit angle at the reference pose, C en,x，0 、C en,y,0 They are respectively at the reference pose C en The x- and y-axis components of ψ n,0 is the directional frequency response function at the reference pose.

7. The robot processing parameter optimization method based on global stability analysis according to claim 6 is characterized in that: According to the coordinate value of the jth tool position, the joint angle, Jacobian matrix, and joint stiffness matrix are calculated through the robot kinematic model to obtain C en,x,j and C en,y,j : The flexibility parameter C at the j-th tool point en for Among them, C rs,tt Represents the translation stiffness matrix, through the global stiffness matrix Get, C θ is the joint stiffness matrix, C rs,rr represents the torsional stiffness matrix, C rs,tr represents the translation-torsion coupling matrix, C rs,rt represents the torsional-translational coupling matrix.

8. The robot processing parameter optimization method based on global stability analysis according to claim 1 is characterized in that: a p,j and a p,lim,j The ratio is: Among them, PI f Indicates the probability of chatter occurrence at the corresponding tool position. When PI f When the value is less than the threshold, chattering occurs. The threshold value range is 1-1.

1.

9. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the robot machining parameter optimization method based on global stability analysis as claimed in any one of claims 1 to 8 are implemented.

10. A robot machining parameter optimization system based on global stability analysis, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes the computer program to implement the steps of the robot machining parameter optimization method based on global stability analysis according to any one of claims 1 to 8.

Images